Journal of Function Spaces The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. New Inner Product Quasilinear Spaces on Interval Numbers Tue, 26 Jul 2016 14:42:05 +0000 Primarily we examine the new example of quasilinear spaces, namely, “ interval space.” We obtain some new theorems and results related to this new quasilinear space. After giving some new notions of quasilinear dependence-independence and basis on quasilinear functional analysis, we obtain some results on interval space related to these concepts. Secondly, we present , and quasilinear spaces and we research some algebraic properties of these spaces. We obtain some new results and provide an important contribution to the improvement of quasilinear functional analysis. Hacer Bozkurt and Yılmaz Yilmaz Copyright © 2016 Hacer Bozkurt and Yılmaz Yilmaz. All rights reserved. Riesz Transform Characterization of Weighted Hardy Spaces Associated with Schrödinger Operators Tue, 26 Jul 2016 13:45:18 +0000 We characterize the weighted local Hardy spaces related to the critical radius function and weights by localized Riesz transforms ; in addition, we give a characterization of weighted Hardy spaces via Riesz transforms associated with Schrödinger operator , where is a Schrödinger operator on () and is a nonnegative function satisfying the reverse Hölder inequality. Hua Zhu Copyright © 2016 Hua Zhu. All rights reserved. Stability of a Quartic Functional Equation in Restricted Domains Tue, 26 Jul 2016 10:03:53 +0000 Let be a real normed space and a Banach space and . We prove the Ulam-Hyers stability theorem for the quartic functional equation in restricted domains. As a consequence we consider a measure zero stability problem of the above inequality when . Jaeyoung Chung and Yu-Min Ju Copyright © 2016 Jaeyoung Chung and Yu-Min Ju. All rights reserved. Existence and Asymptotic Behaviour of Solutions of Differential and Integral Equations in Some Function Spaces 2016 Mon, 25 Jul 2016 12:37:03 +0000 Józef Banaś, Leszek Olszowy, Kishin Sadarangani, Asadollah Aghajani, and Mohamed A. Taoudi Copyright © 2016 Józef Banaś et al. All rights reserved. On the Existence of Coincidence and Common Fixed Point of Two Rational Type Contractions and an Application in Dynamical Programming Mon, 25 Jul 2016 09:05:01 +0000 We establish some coincidence point results for self-mappings satisfying rational type contractions in a generalized metric space. Presented coincidence point theorems weaken and extend numerous existing theorems in the literature besides furnishing some illustrative examples for our results. Finally, our results apply, in particular, to the study of solvability of functional equations arising in dynamic programming. Ahmed H. Soliman and Tamer Nabil Copyright © 2016 Ahmed H. Soliman and Tamer Nabil. All rights reserved. On the Stability of Quadratic Functional Equations in -Spaces Mon, 25 Jul 2016 07:36:51 +0000 The Hyers-Ulam-Rassias stability of quadratic functional equation and orthogonal stability of the Pexiderized quadratic functional equation in -spaces are proved. Xiuzhong Yang Copyright © 2016 Xiuzhong Yang. All rights reserved. SPDIEs and BSDEs Driven by Lévy Processes and Countable Brownian Motions Thu, 21 Jul 2016 11:31:46 +0000 The paper is devoted to solving a new class of backward stochastic differential equations driven by Lévy process and countable Brownian motions. We prove the existence and uniqueness of the solutions to the backward stochastic differential equations by constructing Cauchy sequence and fixed point theorem. Moreover, we give a probabilistic solution of stochastic partial differential integral equations by means of the solution of backward stochastic differential equations. Finally, we give an example to illustrate. Pengju Duan Copyright © 2016 Pengju Duan. All rights reserved. Optimal Bounds for Gaussian Arithmetic-Geometric Mean with Applications to Complete Elliptic Integral Wed, 20 Jul 2016 11:27:25 +0000 We present the best possible parameters and such that the double inequalities , , hold for all with , where , , and are the arithmetic, quadratic, and Gauss arithmetic-geometric means of and , respectively. As applications, we find several new bounds for the complete elliptic integrals of the first and second kind. Hua Wang, Wei-Mao Qian, and Yu-Ming Chu Copyright © 2016 Hua Wang et al. All rights reserved. Singularities for One-Parameter Null Hypersurfaces of Anti-de Sitter Spacelike Curves in Semi-Euclidean Space Tue, 19 Jul 2016 11:09:36 +0000 We consider one-parameter null hypersurfaces associated with spacelike curves. The spacelike curves are in anti-de Sitter 3-space while one-parameter null hypersurfaces lie in 4-dimensional semi-Euclidean space with index 2. We classify the generic singularities of the hypersurfaces, which are cuspidal edges and swallowtails. And we reveal the geometric meanings of the singularities of such hypersurfaces by the singularity theory. Yongqiao Wang, Donghe Pei, and Ruimei Gao Copyright © 2016 Yongqiao Wang et al. All rights reserved. On the Asymptotic Properties of Nonlinear Third-Order Neutral Delay Differential Equations with Distributed Deviating Arguments Mon, 18 Jul 2016 13:36:07 +0000 This paper is concerned with the asymptotic properties of solutions to a third-order nonlinear neutral delay differential equation with distributed deviating arguments. Several new theorems are obtained which ensure that every solution to this equation either is oscillatory or tends to zero. Two illustrative examples are included. Youliang Fu, Yazhou Tian, Cuimei Jiang, and Tongxing Li Copyright © 2016 Youliang Fu et al. All rights reserved. Characterization of Reflexivity by Convex Functions Sun, 17 Jul 2016 12:55:23 +0000 A new convexity property of convex functions is introduced. This property provides, in particular, a characterization of the class of reflexive Banach spaces. Zhenghua Luo and Qingjin Cheng Copyright © 2016 Zhenghua Luo and Qingjin Cheng. All rights reserved. Fixed Point Results Satisfying Rational Type Contraction in -Metric Spaces Sun, 17 Jul 2016 06:54:25 +0000 A unique fixed point theorem for three self-maps under rational type contractive condition is established. In addition, a unique fixed point result for six continuous self-mappings through rational type expression is also discussed. Branislav Z. Popović, Muhammad Shoaib, and Muhammad Sarwar Copyright © 2016 Branislav Z. Popović et al. All rights reserved. A Best Proximity Point Theorem for Generalized Non-Self-Kannan-Type and Chatterjea-Type Mappings and Lipschitzian Mappings in Complete Metric Spaces Thu, 14 Jul 2016 06:32:08 +0000 The purpose of this paper is to provide and study a best proximity point theorem for generalized non-self-Kannan-type and Chatterjea-type mappings and Lipschitzian mappings in complete metric spaces. The significant mapping in a unified form which related to contractive mappings, Kannan-type mappings, and Chatterjea-type mappings is established. We also provide some examples to illustrate the situation corresponding to the main theorem. The main result of this paper can be viewed as a general and unified form of several previously existing results. Kasamsuk Ungchittrakool Copyright © 2016 Kasamsuk Ungchittrakool. All rights reserved. Solutions to Uncertain Volterra Integral Equations by Fitted Reproducing Kernel Hilbert Space Method Wed, 13 Jul 2016 13:17:53 +0000 We present an efficient modern strategy for solving some well-known classes of uncertain integral equations arising in engineering and physics fields. The solution methodology is based on generating an orthogonal basis upon the obtained kernel function in the Hilbert space in order to formulate the analytical solutions in a rapidly convergent series form in terms of their -cut representation. The approximation solution is expressed by -term summation of reproducing kernel functions and it is convergent to the analytical solution. Our investigations indicate that there is excellent agreement between the numerical results and the RKHS method, which is applied to some computational experiments to demonstrate the validity, performance, and superiority of the method. The present work shows the potential of the RKHS technique in solving such uncertain integral equations. Ghaleb Gumah, Khaled Moaddy, Mohammed Al-Smadi, and Ishak Hashim Copyright © 2016 Ghaleb Gumah et al. All rights reserved. Existence of Positive Solution to System of Nonlinear Third-Order Three-Point BVPs Wed, 13 Jul 2016 10:07:22 +0000 We are concerned with the following system of third-order three-point boundary value problems: , , , , , , , and , where and . By imposing some suitable conditions on and , we obtain the existence of at least one positive solution to the above system. The main tool used is the theory of the fixed-point index. Jian-Ping Sun, Xue-Mei Yang, and Ya-Hong Zhao Copyright © 2016 Jian-Ping Sun et al. All rights reserved. Abstract Theorems on Exchange of Limits and Preservation of (Semi)continuity of Functions and Measures in the Filter Convergence Setting Wed, 13 Jul 2016 06:11:26 +0000 We give necessary and sufficient conditions for exchange of limits of double-indexed families, taking values in sets endowed with an abstract structure of convergence, and for preservation of continuity or semicontinuity of the limit family, with respect to filter convergence. As a consequence, we give some filter limit theorems and some characterization of continuity and semicontinuity of the limit of a pointwise convergent family of set functions. Furthermore, we pose some open problems. Antonio Boccuto and Xenofon Dimitriou Copyright © 2016 Antonio Boccuto and Xenofon Dimitriou. All rights reserved. Dual -Mixed Geominimal Surface Area and Related Inequalities Sun, 10 Jul 2016 07:32:44 +0000 The integral formula of dual -geominimal surface area is given and the concept of dual -geominimal surface area is extended to dual -mixed geominimal surface area. Properties for the dual -mixed geominimal surface areas are established. Some inequalities, such as analogues of Alexandrov-Fenchel inequalities, Blaschke-Santaló inequalities, and affine isoperimetric inequalities for dual -mixed geominimal surface areas, are also obtained. Tongyi Ma and Yibin Feng Copyright © 2016 Tongyi Ma and Yibin Feng. All rights reserved. Topological Dual Systems for Spaces of Vector Measure -Integrable Functions Wed, 29 Jun 2016 12:11:24 +0000 We show a Dvoretzky-Rogers type theorem for the adapted version of the -summing operators to the topology of the convergence of the vector valued integrals on Banach function spaces. In the pursuit of this objective we prove that the mere summability of the identity map does not guarantee that the space has to be finite dimensional, contrary to the classical case. Some local compactness assumptions on the unit balls are required. Our results open the door to new convergence theorems and tools regarding summability of series of integrable functions and approximation in function spaces, since we may find infinite dimensional spaces in which convergence of the integrals, our vector valued version of convergence in the weak topology, is equivalent to the convergence with respect to the norm. Examples and applications are also given. P. Rueda and E. A. Sánchez Pérez Copyright © 2016 P. Rueda and E. A. Sánchez Pérez. All rights reserved. Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation Tue, 28 Jun 2016 12:20:35 +0000 This paper investigates Lotka-Volterra system under a small perturbation , . By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near the system has a generalized homoclinic solution exponentially approaching a periodic solution. Yuzhen Mi Copyright © 2016 Yuzhen Mi. All rights reserved. Estimates of Fractional Integral Operators on Variable Exponent Lebesgue Spaces Mon, 27 Jun 2016 07:37:08 +0000 By some estimates for the variable fractional maximal operator, the authors prove that the fractional integral operator is bounded and satisfies the weak-type inequality on variable exponent Lebesgue spaces. Canqin Tang, Qing Wu, and Jingshi Xu Copyright © 2016 Canqin Tang et al. All rights reserved. On Cluster -Algebras Sun, 26 Jun 2016 10:55:03 +0000 We introduce a -algebra attached to the cluster and a quiver . If is the quiver coming from triangulation of the Riemann surface with a finite number of cusps, we prove that the primitive spectrum of times is homeomorphic to a generic subset of the Teichmüller space of surface . We conclude with an analog of the Tomita-Takesaki theory and the Connes invariant for the algebra . Igor V. Nikolaev Copyright © 2016 Igor V. Nikolaev. All rights reserved. A Class of Special Hypersurfaces in Real Space Forms Mon, 20 Jun 2016 10:44:09 +0000 We define the generalized golden- and product-shaped hypersurfaces in real space forms. A hypersurface in real space forms , , and is isoparametric if it has constant principal curvatures. Based on the classification of isoparametric hypersurfaces, we obtain the whole families of the generalized golden- and product-shaped hypersurfaces in real space forms. Yan Zhao and Ximin Liu Copyright © 2016 Yan Zhao and Ximin Liu. All rights reserved. Calculus Rules for -Proximal Subdifferentials in Smooth Banach Spaces Mon, 13 Jun 2016 11:21:09 +0000 In 2010, Bounkhel et al. introduced new proximal concepts (analytic proximal subdifferential, geometric proximal subdifferential, and proximal normal cone) in reflexive smooth Banach spaces. They proved, in -uniformly convex and -uniformly smooth Banach spaces, the density theorem for the new concepts of proximal subdifferential and various important properties for both proximal subdifferential concepts and the proximal normal cone concept. In this paper, we establish calculus rules (fuzzy sum rule and chain rule) for both proximal subdifferentials and we prove the Bishop-Phelps theorem for the proximal normal cone. The limiting concept for both proximal subdifferentials and for the proximal normal cone is defined and studied. We prove that both limiting constructions coincide with the Mordukhovich constructions under some assumptions on the space. Applications to nonconvex minimisation problems and nonconvex variational inequalities are established. Messaoud Bounkhel Copyright © 2016 Messaoud Bounkhel. All rights reserved. Existence of Solutions to a Class of Semilinear Elliptic Problem with Nonlinear Singular Terms and Variable Exponent Mon, 13 Jun 2016 08:13:26 +0000 The authors of this paper prove the existence and regularity results for the homogeneous Dirichlet boundary value problem to the equation with and . The results show the dependence of the summability of in some Lebesgue spaces and on the values of . Ying Chu, Yanchao Gao, and Wenjie Gao Copyright © 2016 Ying Chu et al. All rights reserved. Nonclassical Problem for Ultraparabolic Equation in Abstract Spaces Sun, 12 Jun 2016 11:33:50 +0000 Nonclassical problem for ultraparabolic equation with nonlocal initial condition with respect to one time variable is studied in abstract Hilbert spaces. We define the space of square integrable vector-functions with values in Hilbert spaces corresponding to the variational formulation of the nonlocal problem for ultraparabolic equation and prove trace theorem, which allows one to interpret initial conditions of the nonlocal problem. We obtain suitable a priori estimates and prove the existence and uniqueness of solution of the nonclassical problem and continuous dependence upon the data of the solution to the nonlocal problem. We consider an application of the obtained abstract results to nonlocal problem for ultraparabolic partial differential equation with second-order elliptic operator and obtain well-posedness result in Sobolev spaces. Gia Avalishvili and Mariam Avalishvili Copyright © 2016 Gia Avalishvili and Mariam Avalishvili. All rights reserved. Hausdorff Dimension of a Random Attractor for Stochastic Boussinesq Equations with Double Multiplicative White Noises Thu, 09 Jun 2016 09:38:59 +0000 This paper investigates the existence of random attractor for stochastic Boussinesq equations driven by multiplicative white noises in both the velocity and temperature equations and estimates the Hausdorff dimension of the random attractor. Yin Li, Ruiying Wei, and Donghong Cai Copyright © 2016 Yin Li et al. All rights reserved. Approximation of Analytic Functions by Solutions of Cauchy-Euler Equation Mon, 06 Jun 2016 06:05:57 +0000 We investigate the approximation properties of a special class of twice continuously differentiable functions by solutions of the Cauchy-Euler equation. Soon-Mo Jung Copyright © 2016 Soon-Mo Jung. All rights reserved. Filling Disks of Hayman Type of Meromorphic Functions Tue, 31 May 2016 11:24:34 +0000 We obtain the existence of the filling disks with respect to Hayman directions. We prove that, under the condition , there exists a sequence of filling disks of Hayman type, and these filling disks can determine a Hayman direction. Every meromorphic function of positive and finite order has a sequence of filling disks of Hayman type, which can also determine a Hayman direction of order . Nan Wu and Zuxing Xuan Copyright © 2016 Nan Wu and Zuxing Xuan. All rights reserved. On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials Mon, 30 May 2016 12:29:53 +0000 We provide the proof of a practical pointwise characterization of the set defined by the closure set of the real projections of the zeros of an exponential polynomial with real frequencies linearly independent over the rationals. As a consequence, we give a complete description of the set and prove its invariance with respect to the moduli of the , which allows us to determine exactly the gaps of and the extremes of the critical interval of by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance. J. M. Sepulcre Copyright © 2016 J. M. Sepulcre. All rights reserved. Hadamard Multipliers and Abel Dual of Hardy Spaces Mon, 30 May 2016 12:29:11 +0000 The paper is devoted to the study of Hadamard multipliers of functions from the abstract Hardy classes generated by rearrangement invariant spaces. In particular the relation between the existence of such multiplier and the boundedness of the appropriate convolution operator on spaces of measurable functions is presented. As an application, the description of Hadamard multipliers into is given and the Abel type theorem for mentioned Hardy spaces is proved. Paweł Mleczko Copyright © 2016 Paweł Mleczko. 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